From DE 199 61 451 A1, a balancing device for a tool holder is known in which, in a receptacle opening of a main body that rotates about an axis of rotation, a centering element constructed as a ball sleeve is arranged for centering a coupling shaft of the tool holder. The ball sleeve contains a sleeve-shaped ball cage in which ball-shaped rolling bodies are guided. To be able to pre-tension the ball cage without twisting toward the larger diameter side of the coupling shaft, several compression springs distributed in the circumferential direction are mounted between the ball cage and a support shoulder within the main body. A stop ring of the main body limits the displacement of the ball cage. Due to the compression springs, the ball cage can indeed move along with a defined displacement of the coupling shaft during the tensioning process, but problems with concentricity can be produced due to the greater number of individual parts that can move separately relative to each other.